A small ball undergoes a partially elastic collision with a rough horizontal surface. Assume that friction \(f=\mu N\) during the contact period, where \(N\) is the normal reaction and \(\mu\) is the coefficient of friction.

Find the value of the incoming angle \(\theta\) (in degrees) such that the horizontal range of the ball after hitting the surface is maximized.

\(\)

**Details and Assumptions:**

- Take the coefficient of friction \(\mu = \frac{1}{\sqrt{3}}.\)
- Take the coefficient of restitution \(e=\sqrt{3}-1\).

Inspired from Rajdeep Brahma

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